Results 11 to 20 of about 15,258,586 (276)
Well-posedness of stochastic modified Kawahara equation
Advances in Difference Equations, 2020 In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) $H^{s}(\mathbb{R})$, s≥−1/4 $s\geq -1/4$. Moreover, we get the
P. Agarwal, Abd-Allah Hyder, M. Zakarya
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Global well-posedness for fractional Sobolev-Galpern type equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2021 This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to
Nguyen Huy Tuan +2 more
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Sharp well-posedness for the Benjamin–Ono equation [PDF]
Inventiones Mathematicae, 2023 The Benjamin–Ono equation is shown to be well-posed, both on the line and on the circle, in the Sobolev spaces Hs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
R. Killip, Thierry Laurens, M. Vişan
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Well-posedness of stochastic partial differential equations with fully local monotone coefficients [PDF]
Mathematische Annalen, 2022 Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple V⊆H⊆V∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Michael Röckner +2 more
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Well-posedness for the surface quasi-geostrophic front equation [PDF]
Nonlinearity, 2022 We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter–Shu–Zhang (2021 Pure Appl. Anal. 3 403–72) established well-posedness under a small data condition as well as a convergence condition on an expansion of the ...
Albert Ai, Ovidiu-Neculai Avadanei
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On the well-posedness problem for the derivative nonlinear Schrödinger equation [PDF]
Analysis & PDE, 2021 We consider the derivative nonlinear Schr\"odinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and $L^2$-critical with respect to scaling.
R. Killip, Maria Ntekoume, M. Vişan
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Global well‐posedness for the one‐phase Muskat problem [PDF]
Communications on Pure and Applied Mathematics, 2021 The free boundary problem for a two‐dimensional fluid permeating a porous medium is studied. This is known as the one‐phase Muskat problem and is mathematically equivalent to the vertical Hele‐Shaw problem driven by gravity force.
Hongjie Dong, F. Gancedo, Huy Q. Nguyen
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Local well-posedness for the inhomogeneous nonlinear Schrödinger equation
Discrete and Continuous Dynamical Systems. Series A, 2021 We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation \begin{document}$ i\partial_t u +\Delta u = \mu |x|^{-b}|u|^\alpha u,\; u(0)\in H^s({\mathbb R}^N),\; N\geq 1,\; \mu\in {\mathbb C},\; \; b>0 $\end{document} and \begin ...
L. Aloui, S. Tayachi
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Well-posedness and tamed schemes for McKean-Vlasov Equations with Common Noise [PDF]
The Annals of Applied Probability, 2020 In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients having super-linear growth in the state variable.
C. Kumar +3 more
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